For those of us who hope Britain will engage constructively with the EU, the formation of the Conservative-Liberal Democrat coalition is good news. Even when Conservative leaders expected to win the election outright, they were not planning a confrontational approach to the EU. This is not because David Cameron, William Hague and George Osborne are sympathetic to Brussels – they are all Eurosceptics. Rather, they had worked out that picking fights with the EU would be a distraction from the central task of cutting the budget deficit and reviving the British economy.

That is why, when Cameron laid out his Europe policies in a significant speech on 4 November, he abandoned his pledge of a referendum on the Lisbon treaty. The tone of that speech was moderate, but he still offered several pieces of red meat to his party's Europhobes. In forging the deal with Nick Clegg, Cameron had to discard the reddest of those pieces. Gone is the promise to negotiate opt-outs from the EU treaties on justice and home affairs, the charter of fundamental rights, and social policy. The coalition agreement still retains a commitment "to work to limit the application of the working time directive in the United Kingdom." But that merely requires legislation, and was in any case the policy of the Labour government.

Cameron will hope to satisfy his party's Eurosceptics with three promises in the coalition agreement. One is not to prepare to join the euro during this parliament – but nobody expected Britain to do so. Second is that "the use of any passerelle would require primary legislation", referring to a clause in the Lisbon treaty that allows the governments to agree – by unanimity – to switch decision-making in certain areas to majority voting. However, the act incorporating that treaty into British law already specifies that the passerelle cannot be used without the approval of both houses of parliament.

Third, the coalition has agreed "to amend the 1972 European Communities Act so that any proposed future treaty that transferred areas of power, or competences, would be subject to a referendum on that treaty – a 'referendum lock'". But that is less significant than it sounds, at least in the short and medium term, for there is absolutely no prospect of all the member states agreeing to revise the existing treaties. Angela Merkel has talked of a new treaty to strengthen financial discipline in the euro area, but most governments think it would be crazy to go back to treaty-writing after all the difficulties of getting the Lisbon treaty ratified.

So those three promises do not amount to much. True, there remains a commitment to "examine the case for a United Kingdom sovereignty bill to make it clear that ultimate authority remains with parliament" – but this remains a strange affair, because when one asked the Conservatives what it meant they disagreed. Some said it was merely about putting into UK law the equivalent of the German constitutional court ruling on the Lisbon treaty, which set limits on the transfer of national competences to the EU. But some Eurosceptics said a sovereignty act should be used to strike down EU laws and European court of justice rulings, thereby challenging the supremacy of EU law. The Liberal Democrats will ensure that examining the case for such a bill does not lead to any action, and one senior Conservative has told me the bill will be left on the back-burner.

In short, I do not expect the coalition's policies to create problems for Britain's relations with the EU. If I was Bill Cash, I would be quite annoyed about all this. Indeed, I expect conflict in the coming years between the Conservative leadership (backed by the Liberal Democrats) and hardline Tory Eurosceptics in parliament and in the country at large.

But pro-Europeans should not be too relaxed, because the euro crisis is extremely serious. It will endure for many years and is already undermining trust and solidarity among EU governments. Against the backdrop of this crisis, it will not be easy for the British to develop a more intelligent conversation about Europe.

In any case, there will be events that provoke discord between Britain and the EU. For example, EU finance ministers are due to vote next week on the imposition of strict regulations on hedge funds; Britain may be outvoted, much to the chagrin of the City. Later in the summer, the commission is due to publish a report on the future of the EU budget. Arguments over the EU's finances are guaranteed to create rows.

Of course, a government can often get itself out of a scrape if it has enough allies. For example, it may be able to ensure that a vote is postponed or a text modified. But ever since the Conservatives left the European Peoples Party (EPP), the leading force in the European parliament, to set up a new and smaller rightwing group, the European Conservatives and Reformists, they have not had many powerful friends. The governments of France, Germany, Italy and Poland are all in the EPP. Edward McMillan-Scott, an MEP who recently left the Conservatives for the Liberal Democrats, argued that the Conservatives should now rejoin the EPP, as a means of restoring British influence. I doubt Cameron will do that, given his promise to Bill Cash and other Eurosceptics.

The problem of British influence in Europe is about much more than alignments in the European parliament. In many European capitals there is a growing resentment that is not specifically directed at the Conservatives. There is a feeling that for too long the British have been allowed to get away with picking and choosing those bits of the EU that suit them, without being willing to compromise or show solidarity towards their partners.

For example, ever since the financial crisis led to a big devaluation of the pound against the euro, other Europeans have complained about Britain's "competitive devaluation" distorting the single market unfairly. And then there was the recent decision of Gordon Brown's government not to make even a token contribution to the eurozone's new €450bn bailout fund, which caused resentment; Poland and Sweden, though outside the euro, made modest contributions.

So although the coalition agreement is promising, it will not be enough to ensure a smooth relationship between Britain and the EU. That will require Cameron, Hague and other ministers to engage in some old-fashioned diplomacy, winning allies and making friends. They will need to offer to help other countries with their problems, in order to ensure that favours are returned to Britain. Clegg and other senior Liberal Democrats know that this is how the EU makes progress. They are well-placed to explain this to their coalition partners.